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Answer Key for Quiz 6 (section B) 1. If an = x2n 2n , then an+1 = 2(n...

Answer Key for Quiz 6 (section B). 1. If an = x2n. 2n. , then an+1 = x2(n+1). 2(n + 1). = x2n+2. 2n + 2 . Note that an and an+1 are always positive, because of the ...

Answer Key for Quiz 6 (section B) 1. If an = x2n 2n , then an+1 = 2(n...

Answer Key for Quiz 6 (section B). 1. If an = x2n. 2n. , then an+1 = x2(n+1). 2(n + 1). = x2n+2. 2n + 2 . Note that an and an+1 are always positive, because of the ...

Answer Key for Quiz 6 (section A) 1. If an = (−1)n ... - Bates...

Answer Key for Quiz 6 (section A). 1. If an = (−1)n x2n+1. 2n + 1. , then an+1 = (−1 )n+1 x2(n+1)+1. 2(n +1)+1. = (−1)n+1 x2n+3. 2n + 3 . We could actually ignore ...

Answer Key for Quiz 3 (section B) 1. Following the hint we look at (x...

Answer Key for Quiz 3 (section B). 1. Following the hint we look at. (x + 2)2 − (x + 1)(x + 3) = x2 + 4x + 4 −. ( x2 + 4x + 3. ) = 1. Therefore. ∫ dx. (x + 1)(x + 2)2(x + ...

Answer Key for Quiz 3 (section A) 1. If we substitute u = √ x =...

Answer Key for Quiz 3 (section A). 1. If we substitute u = √ x = x1. 2 , then du = 1. 2 x− 1. 2 dx = dx. 2. √ x. , so that 2 du = dx. √ x . If x = 0 then u = √. 0 = 0, ...

Answer Key for Quiz 2 (section B) 1. Let's start by substituting w =...

Answer Key for Quiz 2 (section B). 1. Let's start by substituting w = x8, in which case dw = 8x7 dx and hence dw. 8. = x7 dx. Then. ∫ x15 cos. ( x8. ) dx = ∫ x8 cos ...

Answer Key for Quiz 2 (section A) 1. We can let u = ln(ln x) and dv...

Answer Key for Quiz 2 (section A). 1. We can let u = ln(ln x) and dv = dx x. , in which case v = ln x (since x is positive) and du = 1 ln x. 1 x dx. Then. ∫ ln (ln x). 1 ...

Answer Key for Quiz 8 (section A) 1. If y = ax8 + bx4 + cx2, then dy...

Answer Key for Quiz 8 (section A). 1. If y = ax8 + bx4 + cx2, then dy dx. = 8ax7 + 4bx3 + 2cx and d2y dx2. = 56ax6 + 12bx2 + 2c. Plugging all this into the ...

Answer Key for Quiz 7 (section A) 1. Since 0 = x(1−x) implies...

Answer Key for Quiz 7 (section A). 1. Since 0 = x(1−x) implies that either x = 0 or x = 1, the curve y = x(1−x) intersects the x-axis at (0, 0) and (1, 0), and is above ...

Answer Key for Quiz 6 1. We have lim x4 − 12x2 + 16x x4 −...

Answer Key for Quiz 6. 1. We have lim x→2 x4 − 12x2 + 16x x4 − x3 − 6x2 + 4x + 8. = 16 − 48 + 32. 16 − 8 − 24+8+8. = 0. 0. , so we need to do something. By ...

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Worksheet 1.16.5 answer key. 1. i) g'x=3x. 2. 4x4=2x. 2. x2. 4x4=2x. 2. x2. 2. 0 for any x value, g'(x) always >0 then we have x belongs to ...

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CSE 101. Practice Midterm: Spring, 2009. Answer Key. Answer all questions. Give informal (at least) proofs for all answers. Grading will be on completeness and ...

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HOMEWORK 7 ANSWER KEY. Exercise 4.2 sum no 11: Prove 1^3+2^3+……………………..+n^3=[n(n+1)/2]^2 for all integers n>=1. Solution: Basis Step: ...

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HOMEWORK 7 ANSWER KEY. Exercise 4.2 sum no 11: Prove 1^3+2^3+……………………..+n^3=[n(n+1)/2]^2 for all integers n>=1. Solution: Basis Step: ...

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KEY FOR QUIZ 2: COMPARATIVE DIGESTIVE SYSTEMS. Topic # 3024. Directions: Answer the following questions as completely as possible. Each question is ...

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Econ Problem Set #2: Trade (answer key). Here we continue the example of Mexico and the US, yellow pine logs and computers. Suppose it costs $500 more to ...

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